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Locality preserving projection on SPD matrix Lie group: algorithm and analysis

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Science China(Information Sciences) 2018年第9期61卷 50-66页

作者： Yangyang LI ruqian lu Academy of Mathematics and Systems Science Key Lab of Management Decision and Information SystemsChinese Academy of Sciences University of Chinese Academy of Sciences

Symmetric positive definite(SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection(LPP)to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.

关键词： manifold learning SPD matrix Lie group locally preserving projection Laplace operator LogEuclidean metric

Applying Ricci flow to high dimensional manifold learning

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Science China(Information Sciences) 2019年第9期62卷 23-36页

作者： Yangyang LI ruqian lu Key Lab of Management Decision and Information Systems Academy of Mathematics and Systems ScienceChinese Academy of Sciences University of Chinese Academy of Sciences

In machine learning, a high dimensional data set such as the digital image of a human face is often viewed as a point set distributed on a differentiable manifold. In many cases, the intrinsic dimension of this manifold is low but the representation dimension of the data points is high. To ease data processing requirements, manifold learning(ML) techniques can be used to reduce a high dimensional manifold(HDM)to a low dimensional one while keeping the essential geometric properties, such as relative distances between points, unchanged. Traditional ML algorithms often assume that the local neighborhood of any point on an HDM is roughly equal to the tangent space at that point. This assumption leads to the disadvantage that the neighborhoods of points on the manifold, though they have a very different curvature, will be treated equally and will be projected to a lower dimensional space. The curvature is a different way of manifold processing, where traditional dimension reduction is ineffective at preserving the *** overcome this obstacle, we perform an "operation" on the HDM using Ricci flow before a manifold’s dimension reduction. More precisely, with the Ricci flow, we transform each local neighborhood of the HDM to a constant curvature patch. The HDM, as a whole, is then transformed into a subset of a sphere with constant positive curvature. We compare the proposed algorithm with other traditional manifold learning algorithms. Experimental results have shown that the proposed method outperforms other ML algorithms with a better neighborhood preserving rate.

关键词： manifold learning Ricci flow Ricci curvature dimension reduction curvature estimation

From knowledge based software engineering to knowware based software engineering

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Science in China(Series F) 2008年第6期51卷 638-660页

作者： lu ruqian JIN Zhi Academy of Mathematics and System Sciences & Institute of Computing Technology Chinese Academy ofSciences Beijing 100190 China

The first part of this paper reviews our efforts on knowledge-based software engineering, namely PROMIS, started from 1990s. The key point of PROMIS is to generate applications automatically based on domain knowledge as well as software knowledge. That is featured by separating the development of domain knowledge from the development of software. But in PROMIS, we did not find an appropriate representation for the domain knowledge. Fortunately, in our recent work, we found such a carrier for knowledge modules, i.e. knowware. Knowware is a commercialized form of domain knowledge. This paper briefly introduces the basic definitions of knowware, knowledge middleware and knowware engineering. Three life circle models of knowware engineering and the design of corresponding knowware implementations are given. Finally we discuss application system automatic generation and domain knowledge modeling on the J2EE platform, which combines the techniques of PROMIS, knowware and J2EE, and the development and deployment framework, i.e. PROMIS/KW＊＊.

关键词： PROMIS knowledge based software engineering knowware J2EE PROMIS/KW** knowware based software engineering

Geometry Flow-Based Deep Riemannian Metric Learning

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IEEE/CAA Journal of Automatica Sinica 2023年第9期10卷 1882-1892页

作者： Yangyang Li Chaoqun Fei Chuanqing Wang Hongming Shan ruqian lu Key Lab of MADIS Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China IEEE Institute of Science and Technology for Brain-Inspired Intelligence and Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence(Ministry of Education)and MOE Frontiers Center for Brain Science Fudan UniversityShanghai 200433 Shanghai Center for Brain Science and Brain-Inspired Technology Shanghai 200031China

Deep metric learning(DML)has achieved great results on visual understanding tasks by seamlessly integrating conventional metric learning with deep neural *** deep metric learning methods focus on designing pair-based distance loss to decrease intra-class distance while increasing interclass ***,these methods fail to preserve the geometric structure of data in the embedding space,which leads to the spatial structure shift across mini-batches and may slow down the convergence of embedding *** alleviate these issues,by assuming that the input data is embedded in a lower-dimensional sub-manifold,we propose a novel deep Riemannian metric learning(DRML)framework that exploits the non-Euclidean geometric structural *** that the curvature information of data measures how much the Riemannian(nonEuclidean)metric deviates from the Euclidean metric,we leverage geometry flow,which is called a geometric evolution equation,to characterize the relation between the Riemannian metric and its *** DRML not only regularizes the local neighborhoods connection of the embeddings at the hidden layer but also adapts the embeddings to preserve the geometric structure of the *** several benchmark datasets,the proposed DRML outperforms all existing methods and these results demonstrate its effectiveness.

关键词： Curvature regularization deep metric learning(DML) embedding learning geometry flow riemannian metric

Networked Knowledge and Complex Networks:An Engineering View

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IEEE/CAA Journal of Automatica Sinica 2022年第8期9卷 1366-1383页

作者： Jinhu Lü Guanghui Wen ruqian lu Yong Wang Songmao Zhang School of Automation Science and Electrical Engineering State Key Laboratory of Software Development EnvironmentBeihang UniversityBeijing 100083 Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Department of Systems Science School of MathematicsSoutheast UniversityNanjing 211189China

Along with the development of information technologies such as mobile Internet,information acquisition technology,cloud computing and big data technology,the traditional knowledge engineering and knowledge-based software engineering have undergone fundamental changes where the network plays an increasingly important *** this context,it is required to develop new methodologies as well as technical tools for network-based knowledge representation,knowledge services and knowledge ***,the term“network”has different meanings in different ***,some breakthroughs in several bottleneck problems of complex networks promote the developments of the new methodologies and technical tools for network-based knowledge representation,knowledge services and knowledge *** paper first reviews some recent advances on complex networks,and then,in conjunction with knowledge graph,proposes a framework of networked knowledge which models knowledge and its relationships with the perspective of complex *** the unique advantages of deep learning in acquiring and processing knowledge,this paper reviews its development and emphasizes the role that it played in the development of knowledge ***,some challenges and further trends are discussed.

关键词： Complex network knowledge graph networked knowledge neural network

Curvature flow learning: algorithm and analysis

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Science China(Information Sciences) 2022年

作者： Yangyang LI ruqian lu Key Lab of MADIS Academy of Mathematics and Systems Science Chinese Academy of Sciences

In order to describe the nonlinear distribution of the image dataset, researchers propose a manifold assumption, called manifold learning (MAL). The geometry information based on a manifold is measured by the Riemannian metric, such as the geodesic distance. Thus, owing to mining the intrinsic geometric structure of the dataset, we need to learn the real Riemannian metric of the embedded manifold. By the Taylor expansion equation of the Riemannian metric, it clearly indicates that the Riemannian metric is relative to the Riemannian curvature. Based on it, we propose a new algorithm to learn the Riemannian metric by adding the curvature information into metric learning. By optimizing the objective function, we obtain a set of iterative equations. We call this model curvature flow. By employing this curvature flow, we obtain a Mahalanobis metric that approaches the Riemannian metric infinitely and can well uncover the intrinsic structure of the embedded manifold. In theory, we analyze several properties of our proposed method, e.g.,the boundedness of the metric and the convergence of curvature flow. To show the effectiveness of our proposed method, we compare our algorithm with several traditional MAL algorithms on three real world datasets. The corresponding results indicate that our proposed method outperforms the other algorithms.

关键词：

ALGEBRAIC SEMANTICS OF PROGRAMS WITH DYNAMIC STRUCTURE

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Science in China,Ser.A 1987年第1期30卷 32-44页

作者：陆汝钤 Institute of Mathematics Academia Sinica

In order to describe algebraic semantics of programs, which do not necessarily terminate, the operations of Σ algebra have been generalized to the case of partial functions on carrier sets. The coweak initial model and the weak terminal model have been proved to exist under certain conditions. However, the prevailing approach fails in the case where the static-structure of the program does not coincide with its dynamic structure. In this paper, a new approach is proposed, which can be used to describe algebraic semantics of programs with dynamic structures as goto statement and nested block. Thus the application of algebraic semantics is extended.

关键词： exp ALGEBRAIC SEMANTICS OF PROGRAMS WITH DYNAMIC STRUCTURE body php open

A direct product decomposition of QMV algebras

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Science China Mathematics 2012年第4期55卷 841-850页

作者： lu Xian 1 ,SHANG Yun 1,& lu ruqian 1,2 1 Institute of Mathematics,Academy of Mathematics and Systems Science,Beijing 100190,China 2 Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China 1. Institute of Mathematics Academy of Mathematics and Systems Science Beijing 100190 China2. Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing 100190 China

We study the direct product decomposition of quantum many-valued algebras (QMV algebras) which generalizes the decomposition theorem of ortholattices (orthomodular lattices).In detail,for an idempo- tent element of a given QMV algebra,if it commutes with every element of the QMV algebra,it can induce a direct product decomposition of the QMV *** the same time,we introduce the commutant C(S) of a set S in a QMV algebra,and prove that when S consists of idempotent elements,C(S) is a subalgebra of the QMV *** also generalizes the cases of orthomodular lattices.

关键词： QMV algebra commutativity idempotent decomposition theorem

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从大数据到大知识

重庆邮电大学学报（自然科学版） 2022年第6期34卷 921-928页

作者：陆汝钤中国科学院{数学与系统科学研究院 MADIS重点实验室}未来人工智能重点实验室北京100190

从大数据获取大知识是未来人工智能要解决的重要科学问题。本文从大数据(BD)概念诞生谈起,回顾了大数据知识工程(BDKE)的提出和大知识概念的出现。然后从(1)大知识(BK)、大知识系统(BKS)、大知识工程(BKE)等概念的基本定义、(2)大知识... 详细信息

从大数据获取大知识是未来人工智能要解决的重要科学问题。本文从大数据(BD)概念诞生谈起,回顾了大数据知识工程(BDKE)的提出和大知识概念的出现。然后从(1)大知识(BK)、大知识系统(BKS)、大知识工程(BKE)等概念的基本定义、(2)大知识规模及其演化、(3)大知识建模、(4)大知识计算、(5)大知识支撑平台、(6)大知识编程语言等六个视角对大知识进行了探讨。最后给出了有关未来研究方向的想法。

关键词：大数据大知识大数据知识工程大知识系统人工智能